Relevant bibliographies by topics / Sign pattern matrices

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Sign pattern matrices'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Sign pattern matrices"

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Eschenbach, Carolyn A., Frank J. Hall, and Zhongshan Li. "Eigenvalue frequency and consistent sign pattern matrices." Czechoslovak Mathematical Journal 44, no. 3 (1994): 461–79. http://dx.doi.org/10.21136/cmj.1994.128471.

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Eschenbach, Carolyn A., Frank J. Hall, and Zhongshan Li. "From real to complex sign pattern matrices." Bulletin of the Australian Mathematical Society 57, no. 1 (1998): 159–72. http://dx.doi.org/10.1017/s0004972700031518.

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This paper extends some fundamental concepts of qualitative matrix analysis from sign pattern classes of real matrices to sign pattern classes of complex matrices. A complex sign pattern and its corresponding sign pattern class are defined in such a way that they generalize the definitions of a (real) sign pattern and its corresponding sign pattern class. A survey of several qualitative results on complex sign patterns is presented. In particular, sign nonsingular complex patterns are investigated. The type of region in the complex plane representing the distribution of the determinants of the
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Stuart, Jeffrey. "Reducible sign k-potent sign pattern matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 197–211. http://dx.doi.org/10.1016/s0024-3795(99)00067-1.

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Stuart, Jeffrey, Carolyn Eschenbach, and Steve Kirkland. "Irreducible sign k-potent sign pattern matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 85–92. http://dx.doi.org/10.1016/s0024-3795(99)00076-2.

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Araújo, C. Mendes, and Juan R. Torregrosa. "Sign pattern matrices that admit P0-matrices." Linear Algebra and its Applications 435, no. 8 (2011): 2046–53. http://dx.doi.org/10.1016/j.laa.2011.03.066.

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Das, Sunil. "Potentially stable and 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative." Electronic Journal of Linear Algebra 37 (July 29, 2021): 562–82. http://dx.doi.org/10.13001/ela.2021.5969.

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Characterization of potentially stable sign pattern matrices has been a long-standing open problem. In this paper, we give some sufficient conditions for tree sign pattern matrices with all edges negative to allow a properly signed nest. We also characterize potentially stable star and path sign pattern matrices with all edges negative. We give a conjecture on characterizing potentially stable tree sign pattern matrices with all edges negative in terms of allowing a properly signed nest which is verified to be true for sign pattern matrices up to order 6. Finally, we characterize all 5-by-5 sp
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Eschenbach, Carolyn A., and Zhongshan Li. "Potentially nilpotent sign pattern matrices." Linear Algebra and its Applications 299, no. 1-3 (1999): 81–99. http://dx.doi.org/10.1016/s0024-3795(99)00163-9.

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Eschenbach, Carolyn. "Idempotence for sign-pattern matrices." Linear Algebra and its Applications 180 (February 1993): 153–65. http://dx.doi.org/10.1016/0024-3795(93)90529-w.

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Lee, Sang-Gu, and Jin-Woo Park. "Sign idempotent sign pattern matrices that allow idempotence." Linear Algebra and its Applications 487 (December 2015): 232–41. http://dx.doi.org/10.1016/j.laa.2015.09.020.

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Yeh, Lina. "Sign pattern matrices that allow a nilpotent matrix." Bulletin of the Australian Mathematical Society 53, no. 2 (1996): 189–96. http://dx.doi.org/10.1017/s0004972700016907.

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Dissertations / Theses on the topic "Sign pattern matrices"

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Kaphle, Krishna. "Spectrally Arbitrary Tree Sign Pattern Matrices." Digital Archive @ GSU, 2006. http://digitalarchive.gsu.edu/math_theses/17.

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A sign pattern (matrix) is a matrix whose entries are from the set {+,–, 0}. A sign pattern matrix A is a spectrally arbitrary pattern if for every monic real polynomial p(x) of degree n there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). All 3 × 3 SAP's, as well as tree sign patterns with star graphs that are SAP's, have already been characterized. We investigate tridiagonal sign patterns of order 4. All irreducible tridiagonal SAP's are identified. Necessary and sufficient conditions for an irreducible tridiagonal pattern to b
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Johansson, Robert. "Pattern Avoidance in Alternating Sign Matrices." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7936.

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<p>This thesis is about a generalization of permutation theory. The concept of pattern avoidance in permutation matrices is investigated in a larger class of matrices - the alternating sign matrices. The main result is that the set of alternating sign matrices avoiding the pattern 132, is counted by the large Schröder numbers. An algebraic and a bijective proof is presented. Another class is shown to be counted by every second Fibonacci number. Further research in this new area of combinatorics is discussed.</p>
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Demir, Nilay Sezin. "Spectrally Arbitrary and Inertially Arbitrary Sign Pattern Matrices." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/math_theses/26.

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A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are then investigated, with a special
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Merid, Assefa D. "Sign Pattern Matrices That Require Almost Unique Rank." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/47.

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A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrixA, the sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost unique rank, that is to say, the sign patterns A s
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Kim, Paul J. "On the 4 by 4 Irreducible Sign Pattern Matrices that Require Four Distinct Eigenvalues." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/101.

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A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive(respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B: sgn(B) = A}. An n by n sign pattern matrix A requires all distinct eigenvalues if every real matrix whose sign pattern is represented by A has n distinct eigenvalues. In this thesis, a number of sufficient and/or necessary conditions for a sign pattern to reuiqre all distin
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Mohindru, Preeti. "Sign Pattern Matrices and Semirings." Thesis, 2011. http://hdl.handle.net/10214/3124.

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Sign pattern theory examines what can be said about a matrix if one knows the signs of all or some of its entries but not the exact values. Since all we know is the sign of each entry, we can write these sign patterns as matrices whose entries come from the set {+1, -1, 0, #}, where # is used for an unknown sign. Semirings satisfy all properties of rings with unity except the existence of additive inverses. The set {+1, -1, 0, #} can be viewed as a commutative semiring in natural way. In the thesis, we give a semiring version of the Cayley-Dickson construction which allows one to construct t
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Grundy, David A. "Potential stability of sign pattern matrices." Thesis, 2010. http://hdl.handle.net/1828/3179.

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An n × n sign pattern A is potentially stable (PS) if there exists a real matrix A having the sign pattern A and with all its eigenvalues having negative real parts. The identification of non-trivial necessary and sufficient conditions for potential stability remains a long standing open problem. Here we review some of the previous results and give simplified proofs for some of these results. Three techniques are given for the construction of larger order PS sign patterns from given PS sign patterns. These techniques are: construction of a sign pattern that allows a nested sequence of prop
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Chen, Wei Xu, and 陳威旭. "Tree sign pattern matrices that require k zero eigenvalues." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/60105965548517790328.

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Gao, Wei. "Minimum Ranks and Refined Inertias of Sign Pattern Matrices." 2016. http://scholarworks.gsu.edu/math_diss/32.

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A sign pattern is a matrix whose entries are from the set $\{+, -, 0\}$. This thesis contains problems about refined inertias and minimum ranks of sign patterns. The refined inertia of a square real matrix $B$, denoted $\ri(B)$, is the ordered $4$-tuple $(n_+(B), \ n_-(B), \ n_z(B), \ 2n_p(B))$, where $n_+(B)$ (resp., $n_-(B)$) is the number of eigenvalues of $B$ with positive (resp., negative) real part, $n_z(B)$ is the number of zero eigenvalues of $B$, and $2n_p(B)$ is the number of pure imaginary eigenvalues of $B$. The minimum rank (resp., rational minimum rank) of a sign pattern matrix $
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Books on the topic "Sign pattern matrices"

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Topics in random matrix theory. American Mathematical Society, 2012.

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Book chapters on the topic "Sign pattern matrices"

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van den Driessche, P. "Sign Pattern Matrices." In Advanced Courses in Mathematics - CRM Barcelona. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70953-6_2.

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Hall, Frank, and Zhongshan Li. "Sign Pattern Matrices." In Discrete Mathematics and Its Applications. Chapman and Hall/CRC, 2013. http://dx.doi.org/10.1201/b16113-48.

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Hall, Frank J., and Zhongshan Li. "Sign Pattern Matrices." In Handbook of Linear Algebra. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420010572-33.

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Hall, Frank, and Zhongshan Li. "Sign Pattern Matrices." In Handbook of Linear Algebra. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420010572.ch33.

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"The inverse sign pattern graph." In Matrices of Sign-Solvable Linear Systems. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511574733.010.

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"Chapter 2. Generalized Inverses of Partitioned Matrices." In Sign Pattern for Generalized Inverses. EDP Sciences, 2021. http://dx.doi.org/10.1051/978-2-7598-2600-1.c004.

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"Chapter 2. Generalized Inverses of Partitioned Matrices." In Sign Pattern for Generalized Inverses. EDP Sciences, 2021. https://doi.org/10.1051/978-2-7598-2599-8.c004.

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"Chapter 3. SNS and S2NS Matrices." In Sign Pattern for Generalized Inverses. EDP Sciences, 2021. http://dx.doi.org/10.1051/978-2-7598-2600-1.c005.

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"Chapter 3. SNS and S2NS Matrices." In Sign Pattern for Generalized Inverses. EDP Sciences, 2021. https://doi.org/10.1051/978-2-7598-2599-8.c005.

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"Matrix sign patterns." In The Mutually Beneficial Relationship of Graphs and Matrices. American Mathematical Society, 2011. http://dx.doi.org/10.1090/cbms/115/06.

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